1. Technical Field of the Invention
The present Invention relates to hydrocarbon well stimulation, and more particularly to methods and processes for optimal design of hydraulic fracturing jobs, and in particular, to methods and processes for selecting the optimal amount of proppant-carrying fluid to be pumped into the fracture (which is a crucial parameter in hydraulic fracturing) wherein these design parameters are obtained, ultimately from a priori formation/rock parameters, from pressure-decline data obtained during both linear and radial flow regimes, and by analogy with a related problem in heat transfer.
2. The Prior Art
The present Invention relates generally to hydrocarbon (petroleum and natural gas) production from wells drilled in the earth. Obviously, it is desirable to maximize both and the overall recovery of hydrocarbon held in the formation and the rate of flow from the subsurface formation to the surface, where it can be recovered. One set of techniques to do this is referred to as stimulation techniques, and one such technique, "hydraulic fracturing," is the subject of the present Invention. The rate of flow, or "production" of hydrocarbon from a geologic formation is naturally dependent on numerous factors. One of these factors is the radius of the borehole. As the radius of the borehole increases, the production rate increases, everything else being equal. Another factor, related to the first, is the flowpaths available to the migrating hydrocarbon.
Drilling a hole in the subsurface is expensive--which limits the number of wells that can be economically drilled--and this expense only generally increases as the size of the hole increases. Additionally, a larger hole creates greater instability to the geologic formation, thus increasing the chances that the formation will shift around the wellbore and therefore damage the wellbore (and at worse collapse). So, while a larger borehole will, in theory, increase hydrocarbon production, it is impractical, and there is a significant downside. Yet, a fracture or large crack within the producing zone of the geologic formation, originating from and radiating out from the wellbore, can actually increase the "effective" (as opposed to "actual") wellbore radius, thus, the well behaves (in terms of production rate) as if the entire wellbore radius were much larger.
Fracturing (generally speaking, there are two types, acid fracturing and propped fracturing, the latter is of primary interest here) thus refers to methods used to stimulate the production of fluids resident in the subsurface, e.g., oil, natural gas, and brines. Hydraulic fracturing involves literally breaking or fracturing a portion of the surrounding strata, by injecting a specialized fluid into the wellbore directed at the face of the geologic formation at pressures sufficient to initiate and/or extend a fracture in the formation. More particularly, a fluid is injected through a wellbore; the fluid exits through holes (perforations in the well casing) and is directed against the face of the formation at a pressure and flow rate sufficient to overcome the in situ stress (a.k.a. the "minimum principal stress) and to initiate and/or extend a fracture(s) into the formation. Actually, what is created by this process is not always a single fracture, but a fracture zone, i.e., a zone having multiple fractures, or cracks in the formation, through which hydrocarbon can more readily flow to the wellbore.
In practice, fracturing a well is a highly complex operation performed with the exquisite orchestration of over a dozen large trucks, roughly the same number of highly skilled engineers the technicians, a mobile laboratory for real-time quality assurance, and powerful integrated computers that monitor pumping rates, downhole pressures, etc. During a typical fracturing job, over 350,000 pounds of fluid will be pumped at extraordinarily high pressures (exceeding the minimum principal stress) down a well, to a pinpoint location, often thousands of feet below the earth's surface. Moreover, during the fracturing process, constant iterations of fluid level, pumping rates, and pumping times are performed in order to maximize the fracture zone, and minimize the damage to the formation.
A typical fracture zone is shown in context, in FIG. 1. The actual wellbore--or hole in the earth into which pipe is placed through which the hydrocarbon flows up from the hydrocarbon-bearing formation to the surface--is shown at 10, and the entire fracture zone is shown at 20. The vertical extent of the hydrocarbon-producing zone is ideally (though not generally) coextensive with the fracture-zone height (by design). These two coextensive zones are shown bounded by 22 and 24. The fracture is usually created in the producing zone of interest (rather than another geologic zone) because holes or perforations, 26-36, are deliberately created in the well casing beforehand; thus the fracturing fluid flows vertically down the wellbore and exits through the perforations.
Typically, creating a fracture in a hydrocarbon-bearing formation requires a complex suite of materials. Most often, four crucial components are required: a carrier fluid, a viscosifier, a proppant, and a breaker. A fifth component is sometimes added, whose purpose is to control leak-off, or migration of the fluid into the fracture face. Roughly, the purpose of the first component is to first create/extend the fracture, then once it is opened enough, to deliver proppant with time varying concentrations into the fracture, which keeps the fracture from closing once the pumping operation is completed. A first fluid termed as pad fluid is injected, and actually creates/extends the fracture. Then carrier fluid together with proppant material is injected into the fractured formation. The carrier fluid is simply the means by which the proppant and breaker are carried into the formation. It should be noted that the pad fluid may or may not be the same as the carrier fluid. Numerous substances can act as a suitable carrier fluid, though they are generally aqueous-based solutions that have been either gelled or foamed (or both). Thus, the carrier fluid is often prepared by blending a polymeric gelling agent with an aqueous solution (sometimes oil-based, sometimes a multi-phase fluid is desirable); often, the polymeric gelling agent is a solvatable polysaccharide, e.g., galactomannan gums, glycomannan gums, and cellulose derivatives. The purpose of the solvatable (or hydratable) polysaccharides is to thicken the aqueous solution so that solid particles known as "proppant" (discussed below) can be suspended in the solution for delivery into the fracture. Thus the polysaccharides function as viscosifiers, that is, they increase the viscosity of the aqueous solution by 10 to 100 times, or even more. During high temperature applications, a cross-linking agent is further added which further increases the viscosity of the solution. The borate ion has been used extensively as a crosslinking agent for hydrated guar gums and other galactomannans to form aqueous gels, e.g., U.S. Pat. No. 3,059,909. Other demonstrably suitable cross-linking agents include: titanium (U.S. Pat. No. 3,888,312), chromium, iron, aluminum, and zirconium (U.S. Pat. No. 3,301,723). More recently, viscoelastic surfactants have been developed which obviates the need for thickening agents, and hence cross-linking agents, see, e.g., U.S. Pat. No. 5,551,516; U.S. Pat. No. 5,258,137; and U.S. Pat. No. 4,725,372, all assigned/licensed to Schlumberger Dowell.
The purpose of the proppant is to keep the newly fractured formation in that fractured state, i.e., from re-closing after the fracturing process is completed; thus, it is designed to keep the fracture open--in other words to provide a permeable path for the hydrocarbon to flow through the fracture and into the wellbore. More specifically, the proppant provides channels within the fracture through which the hydrocarbon can flow into the wellbore and therefore be withdrawn or "produced." Typical material from which the proppant is made includes sand (e.g. 20-40 mesh), bauxite, synthetic materials of intermediate strength, and glass beads. The proppant can also be coated with resin to help prevent proppant flowback in certain applications. Thus, the purpose of the fracturing fluid generally is two-fold: (1) to create or extend an existing fracture through high-pressure introduction into the geologic formation of interest; and (2) to simultaneously deliver the proppant into the fracture void space so that the proppant can create a permanent channel through which the hydrocarbon can flow to the wellbore. Once this second step has been completed, it is desirable to remove the fracturing fluid from the fracture--its presence in the fracture is deleterious, since it plugs the fracture and therefore impedes the flow hydrocarbon. This effect is naturally greater in high permeability formations, since the fluid can readily fill the (larger) void spaces. This contamination of the fracture by the fluid is referred to as decreasing the effective fracture length. And the process of removing the fluid from the fracture once the proppant has been delivered is referred to as "fracture clean-up." For this, the final component of the fracture fluid becomes relevant: the breaker. The purpose of the breaker is to lower the viscosity of the fluid so that it is more easily removed fracture.
Thus, once the well has been drilled, fractures are often deliberately introduced in the formation, as a means of stimulating production, by increasing the effective wellbore radius. The crucial parameters in any hydraulic fracturing job--indeed, perhaps the most important parameters--are the amount of pad fluid and the proppant schedule. The consequences of using too little or too much are severe, and may dramatically affect well performance. If too little pad fluid is used the fracture will not propagate--this is undesirable for obvious reasons. Again, the goal is to achieve the largest possible fracture to fully exploit the drainage basin.
And yet using too much pad fluid--relative to the amount of proppant--is also undesirable. Again, the goal is to create a very large fracture; however, propagating a fracture by injecting fluid into the formation is of nominal value unless that fracture is fully loaded with proppant, otherwise it will immediately close up. In other words, the fracturing fluid, as it is extends the fracture, must carry with it sufficient proppant at that fracture frontier, otherwise, the fracture will simply close up once the fracturing fluid has leaked off into the formation. Therefore, one way to view the deleterious effect of too much fracturing fluid is that it results in a very dilute fracturing fluid-proppant mixture. Thus, as the fluid propagates the fracture, it leaves relatively little proppant in place to keep the fracture open. Put another way, too much fluid causes the fracture front migrate in advance of the proppant front. If the proppant does not plug the tip as it is created by the advancing fluid front, then this portion of the fracture will just close up, as if it were never created.
Therefore, selecting the precise amounts of fracturing fluid and proppant, and the precise ratio of the two, is of extraordinary importance to optimal fracture design, and therefore to overall hydrocarbon production from that reservoir.
The primary objective of the present Invention is optimizing fracture design. "Fracture design" refers to selecting the ideal amounts of fracturing fluid and proppant to pump into the formation. These ideal amounts are highly sensitive to formation parameters, as well as the fracturing fluid type, thus, they need to be selected for each fracturing job separately. When fracturing fluid is pumped into a fracture, it (heuristically) does two things. One, it propagates the fracture. And two, it leaks off into the surrounding formation. The leak-off rate--which is a function of the pumping pressures, the formation geology (i.e., rock type) and the type of fracturing fluid used--is an absolutely crucial parameter for proper fracture design. The reason is that the more fluid that leaks off that occurs, the more fluid that must be pumped into the formation to propagate the fracture. Therefore, in order to design a proper fracture job--that is, how much fracturing fluid to use--one needs to know how much of the fluid (and at what rate) that is pumped into the formation, will be lost into the formation. Thus, the leak-off rate--which again, is unique to a particular formation, and depends upon the type of fluid--is of crucial importance in fracture design. Indeed, the first step in a fracturing job is typically a calibration test, from which the engineer ultimately determines the amount of fracturing fluid to use in the fracturing job.
Leak-off is conceptually separable into two types: Carter leak-off and spurt. FIG. 2 is a cross-sectional view showing certain features of an ordinary fracture. The arrows are flow lines showing the flow path of fracturing fluid from the fracture into the formation. The flow lines represented as 30-38 are more or less perpendicular to the direction of fracture propagation; leak off in this direction is known as "Carter leak-off." (Carter leak-off need not be solely perpendicular, though). The flow lines represented as as 40-48 depict the second type of leak-off, known as "spurt." As evidenced by FIG. 2, this type of leak off occurs right at the fracture frontier. The fluid loss due to spurt accounts for a substantial portion of the fluid loss in cases where a filter case if formed due to pumping crosslinked gel in a high permeability formation.
Depending upon the formation geology (i.e., rock type) spurt can comprise the overwhelming fraction of the total leak-off (compared with Carter leak-off). For instance, in loose unconsolidated formations (&gt;1 Darcy), the skilled engineer would more than likely select a cross-linked hydroxy propyl guar with borate ion gel which would form a tight, quickly forming, nearly impermeable filter cake over the formation face opposing the fracture, in order to prevent fracturing fluid leak-off in the subsequent step of the process--i.e, fracturing fluid carrying the proppant is pumped into the fracture. In this scenario, Carter leak-off is substantially diminished due to the filter cake, thus the majority of the fluid loss occurs via spurt. (In contrast water-based fracturing fluids such as an aqueous solution of KCl, used in low permeability formations, do not cause wall building and therefore, very little leak off is attributable to spurt in these circumstances).
And yet, despite the importance of a precise knowledge of leak-off to proper fracture design, and despite the significant contribution to total leak-off from spurt, no satisfactory method exists for determining the amount of fracturing fluid loss from spurt. The only satisfactory fluid-loss estimation techniques involve determining Carter leak off; these rely upon rough non-analytical estimations of spurt (often mere guesses). Indeed, most minifrac analysis techniques ignore the effect of spurt loss--even though it may comprise the greater source of fluid loss among the two possible sources.
The first attempt to consider spurt loss was presented in K. G. Nolte, A General Analysis of Fracturing Pressure Decline With Application to Three Models, SPE Formation Evaluation, December 1986, p. 571-83. Yet no objective, reproducible system to determine this parameter is available in the state-of-the art. Years later, M. Y. Souliman, in U.S. Pat. No. 5,305,211, assigned to Halliburton, presented a numerical technique for determining spurt loss. Despite its identical goal, the method presented in '211 differs in several substantial respect from the present Invention. More precisely, the present Invention differs from the '211 patent with respect to fundamental concept, physical steps to determine spurt, the techniques following spurt determination, and the accuracy and applicability of the technique.
The present Invention discloses and claims a method for determining spurt from the effect of this fluid-loss mechanism on linear flow slope. Thus a suitable theoretical model is constructed in which fluid loss occurs, in the absence of spurt. The results from this theoretical model are then compared with the normalized real-world data (i.e., fluid loss occurs both due to Carter leak-off and spurt) to obtain a correction that accounts for fluid loss due to spurt. By contrast, the method of the '211 patent determines spurt from closure time. In fact, the '211 patent actually teaches away, or would inevitably discourage one from considering the present Invention: e.g., "Consequently, pressure decline with time following shut-in will yield no information on spurt loss." (c. 6, 1. 20). Thus, the '211 patent relies on closure time to determine spurt--e.g., a higher spurt loss will naturally lead to a lower closure time. According to the '211 patent, the discrepancy between the closure time that would have been observed in the absence of filter cake formation on the fracture face (due to fluid leak-off) and the actual or observed closure time (in the presence of spurt) is used to deduce spurt. Embedded in this methodology is the assumption that the difference between ideal and observed closure time is due solely to spurt. In fact, factors other than spurt may substantially affect closure time, e.g., a change in fracture area after shut-in.
In addition, the present Invention is based on a combination of reservoir-based and fracture-based parameters. Therefore, the method/process of the present Invention requires a two-step approach: a first and a second injection event. Thus, the reservoir fluid-loss coefficient (a function of reservoir mobility) is determined from a first injection event (from which radial flow-based parameters are obtained) for later use in conjunction with linear flow slope and closure parameters obtained during the second-injection event (from which linear flow-based parameters are obtained).
Third, the present Invention also differs from the '211 patent with respect to the post-spurt determination--i.e., how the parameter is applied. In the present Invention, a single mathematical relationship relates linear flow slope, leak-off coefficient, closure pressure, reservoir pressure, and reservoir fluid-loss coefficient, to obtain spurt. Following a determination of spurt, one aspect of the present Invention teaches that the fracture length then be determined from several a priori reservoir parameters and other parameters already obtained (during both first and second injection events) in accordance with the present Invention. One purpose of determining fracture length is that it helps compare a reservoir-based estimate with the model (of the present Invention) estimate. From this comparison, an accurate estimate of fracture compliance can be obtained, therefore further ameliorating model-dependent error. By contrast in the approach taught in the '211 patent, spurt is determined by simultaneously solving a system of five equations. Yet the equations are dependent on a particular fracture-geometry model, and no independent validation exists.
Finally, the method/process disclosed and claimed here is likely to be more accurate than that taught in the '211 patent. Again, one reason is that model dependence is reduced since the present Invention subsumes numerous independent validation, and cross-validation means (e.g., through fracture-dimension comparison). In addition, the method/process of the present Invention is less sensitive to the estimate of closure parameters--again, the '211 patent depends upon them entirely. The present Invention teaches using reservoir parameters in synergy with linear flow-based parameters, rather than rely solely upon fracture closure.
Thus, in contrast to the present Invention, the '211 patent is not based on a theoretical model derived from a well-characterized problem, it does not determine spurt based on parameters determined during both radial and linear flow regimes, and it does not subsume multiple validation and cross-validation means.
Thus, without a reliable means to determine spurt, the estimate of leak off behavior may poorly mimic reality, and therefore, the total amount of fracturing fluid required to optimum fracture design cannot be determined. Additional limitations (other than spurt) in the state-of-the art fracture calibration, to which the present Invention is directed will now be discussed. First, specialized plots (e.g., square root shut-in time) offer multiple possibilities from which to select closure pressure; therefore, these methods require highly subjective interpretation. This shall be demonstrated by example, later in the Application. Second, the fracturing fluid leak-off computation depends upon fracture compliance, yet accurate estimates prior to calibration are often not available.
Therefore, one object of the present Invention is to provide a reliable, empirically based method, that integrates multiple-validation means, to determine fracturing fluid leak-off due to spurt--i.e., fluid lost at the fracture frontier, or tip--and also a highly reliable value for fracture efficiency.
Of equal importance is the second object of the present Invention which is to provide a validation of the fracture length obtained using the conventional approach (dependent on fracture compliance) with a reservoir perspective. The comparison helps validate the fracture compliance and consequently obtain a highly reliable value for leakoff.